The vertex of an angle measuring 32° is in the exterior of a circle and its sides are secants of the circle. If the sum of the measures of the intercepted arcs is 180°, find the measure of each intercepted arc.
lol ik y'all already ran out of brainy questions so the answers are 58 and 122
To solve this problem, we need to understand the relationship between angles and arcs in a circle:
1. The measure of an angle formed by two secants that intersect outside the circle is equal to half the difference of the measures of the intercepted arcs.
In this case, the angle measures 32°, so let's call the difference between the intercepted arcs x. Therefore, the measure of each intercepted arc can be expressed as (x/2).
2. The sum of the measures of the intercepted arcs is 180°.
According to the problem, the sum of the intercepted arcs is 180°. So, we can write an equation: x + (x/2) = 180.
Now, let's solve the equation to find the value of x and then determine the measure of each intercepted arc:
Multiply the entire equation by 2 to get rid of the fraction:
2x + x = 360.
Combine like terms:
3x = 360.
Divide both sides by 3:
x = 120.
Now that we have the value of x, we can find the measure of each intercepted arc:
Each intercepted arc = (x/2)
Each intercepted arc = (120/2)
Each intercepted arc = 60°.
Therefore, each intercepted arc measures 60°.
Ur dumb bro
what do you mean by "in the exterior of a circle"? How far away from the circle?
All we know is that we have an inscribed polygon with one side being the diameter of the circle. How many sides? Are they all equal (except for the diameter, of course)?